Select The Correct Answer.Which Of The Following Represents A Constant From The Expression 15 X 2 + 2 X + 9 15x^2 + 2x + 9 15 X 2 + 2 X + 9 ?A. 2 B. 9 C. 15 D. 24

In algebra, a constant is a value that does not change and is often represented by a number or a variable raised to the power of zero. When dealing with algebraic expressions, it's essential to identify the constants to simplify and solve equations. In this article, we'll explore the concept of constants and determine which of the given options represents a constant from the expression $15x^2 + 2x + 9$.

What are Constants?

Constants are values that remain unchanged in an algebraic expression. They can be numbers, variables raised to the power of zero, or even complex numbers. Constants are often denoted by a single letter or symbol, such as $a$, $b$, or $c$. In the expression $15x^2 + 2x + 9$, the constants are the values that do not contain the variable $x$.

Identifying Constants in the Expression

Let's examine the expression $15x^2 + 2x + 9$ and identify the constants.

• The first term, $15x^2$, contains the variable $x$ raised to the power of 2. Therefore, it is not a constant.
• The second term, $2x$, contains the variable $x$ raised to the power of 1. Therefore, it is not a constant.
• The third term, $9$, is a number and does not contain the variable $x$. Therefore, it is a constant.

Conclusion

Based on the definition of constants and the analysis of the expression $15x^2 + 2x + 9$, we can conclude that the constant term is $9$. Therefore, the correct answer is:

B. 9

Additional Examples

To further reinforce the concept of constants, let's consider a few more examples.

• In the expression $3x^2 + 4x - 5$, the constants are $3$ and $-5$.
• In the expression $2x^3 - 3x^2 + 7$, the constants are $-3$ and $7$.
• In the expression $x^2 + 2x + 1$, the constants are $1$.

Tips for Identifying Constants

When dealing with algebraic expressions, here are some tips to help you identify constants:

• Look for terms that do not contain the variable.
• Check if the term is a number or a variable raised to the power of zero.
• Be careful not to confuse constants with coefficients, which are numbers that multiply the variable.

Conclusion

In the previous article, we discussed the concept of constants in algebraic expressions and identified the constant term in the expression $15x^2 + 2x + 9$. In this article, we'll address some frequently asked questions (FAQs) about constants in algebra.

Q: What is the difference between a constant and a coefficient?

A: A constant is a value that remains unchanged in an algebraic expression, while a coefficient is a number that multiplies the variable. For example, in the expression $3x^2 + 4x - 5$, the constant is $-5$ and the coefficients are $3$ and $4$.

Q: Can a constant be a variable raised to the power of zero?

A: Yes, a constant can be a variable raised to the power of zero. For example, in the expression $x^0 + 2x + 3$, the constant is $x^0$, which is equal to $1$.

Q: How do I identify constants in an algebraic expression?

A: To identify constants in an algebraic expression, look for terms that do not contain the variable. Check if the term is a number or a variable raised to the power of zero. Be careful not to confuse constants with coefficients, which are numbers that multiply the variable.

Q: Can a constant be a complex number?

A: Yes, a constant can be a complex number. For example, in the expression $3x^2 + 4x - 5i$, the constant is $-5i$, which is a complex number.

Q: How do I simplify an algebraic expression with constants?

A: To simplify an algebraic expression with constants, combine like terms and eliminate any constants that are added or subtracted. For example, in the expression $3x^2 + 4x - 5 + 2x^2 - 3x + 5$, the constants can be combined as follows:

$3x^2 + 2x^2 = 5x^2$ $4x - 3x = x$ $-5 + 5 = 0$

The simplified expression is $5x^2 + x$.

Q: Can a constant be a fraction?

A: Yes, a constant can be a fraction. For example, in the expression $3x^2 + 4x - 1/2$, the constant is $-1/2$, which is a fraction.

Q: How do I solve an equation with constants?

A: To solve an equation with constants, isolate the variable by performing algebraic operations. For example, in the equation $3x^2 + 4x - 5 = 0$, the constants can be eliminated by subtracting $-5$ from both sides:

$3x^2 + 4x = 5$

The equation can then be solved using algebraic methods.

Conclusion

In conclusion, constants are values that remain unchanged in an algebraic expression. By understanding the concept of constants and how to identify them, you can simplify and solve equations more efficiently. In this article, we've addressed some frequently asked questions (FAQs) about constants in algebra and provided examples to illustrate the concepts.